I do have a 1.4X, and I did forget that the 5D III does allow AF at f/8 since the firmware update in April... so that is an option. That was always reserved for 1D series bodies in the past.
Brant - Have you tried your 100-400mm with a Canon 1.4X on your 5D III?
Pat
5DS R, 1D X, 7D, Sigma 10-20mm f/4-5.6, 24mm f/1.4L II, 16-35mm f/4L IS, 24-105mm f/4L, 50mm f/1.8, 100mm Macro f/2.8L, 70-200mm f/2.8L IS II, 100-400mm f/4.5-5.6L, 580EX-II
flickr
The short answer is not yet with AF. In February, I sent the 1.4x TC I bought back to shave a little off the investment I was making at the time and because I was getting similar IQ results with cropping on the 5DIII without the 1.4 TC as with it in the tests I did. Those tests were with the 100-400L, tripod mount, and manual focused in live view. As the 100-400L has a pretty short focus throw, I am probably due to give it another chance now that I can try it with AF. I'll definitely do so before you are ready to buy, but that sounds like it is next spring. Let me know.
But I have shot a number of birds with just the 100-400L and 5DIII and haven't really missed the reach. I do notice it on far away subjects, but, for example, this shot was at 44 meters and for some reason @ 365 mm:
small-5032-2 by kayaker72, on Flickr
It isn't yet a 100% crop, but it is getting close.